Here's a thought. Quebec's lieutenant-governor has retired, and La Presse columnist Michel-C Auger proposes the Assemblée Nationale should elect a successor (or organize some other form of election for the post) and ask the prime minister to appoint whomever wins. As he says, should we have PR and endless minority coalitions, the choosing-a-premier function of lieutenant governors will grow in importance, and their legitimacy will become crucial.
Course you never see any of the PR gurus thinking through issues like these.